It is no guarentee, but temping/contractor work is how I got into Big Tech. I did a good enough job and impressed enough people the team was willing to pick me up full time.
However, I would warn the OP that the most important thing is to start building a portfolio of reliablity. Temping/contracting can be demeaning- you ABSOLUTELY are a second class citizen on the teams. You will be assigned the least strategic work, because if it was strategic they would have an FTE do it. The key thing is to push through and build up a basis of trust- you can do whatever is needed, when it is needed, even if its not what you wanted, and do so in a way that people enjoy being around you.
The issue is that if you haven't had a job in a couple months, you can get tagged as unemployable. There's no point in telling people what you did six months ago if they are going to assume that you can't do anything (that you're not doing at the moment).
All you have to do to get past that is subordinate everything else to being employed for the moment. It's a lesson in prioritization. You can get on the treadmill nearly as fast as you got off of it. At least if you think 6 months to a year is reasonable speed.
However, I would warn the OP that the most important thing is to start building a portfolio of reliablity. Temping/contracting can be demeaning- you ABSOLUTELY are a second class citizen on the teams. You will be assigned the least strategic work, because if it was strategic they would have an FTE do it. The key thing is to push through and build up a basis of trust- you can do whatever is needed, when it is needed, even if its not what you wanted, and do so in a way that people enjoy being around you.